Aim. The lead-field method is an efficient approach for computing the ECG and offers a substantial speed-up over the pseudo-bidomain model. Since lead fields do not depend on cardiac activation, they can be precomputed once and reused for any excitation pattern, substantially reducing the cost of repeated ECG simulations. However, the computational cost of the lead-field method scales linearly with the number of electrodes, which becomes a limiting factor in applications where hundreds of electrodes are required. In this work, we propose a neural network surrogate that approximates the lead field gradient as a continuous function of spatial coordinates, electrode position, and a compact encoding of the heart-torso anatomy.
Methods. Biventricular statistical shape models were combined with the MPII Human Shape Atlas to construct a joint representation of heart and torso geometry. Training and test cohorts of 100 and 10 samples, respectively, were generated by sampling the first 10 principal components of both heart and torso along with cardiac orientation angles using Latin Hypercube Sampling. Lead fields were calculated using FEM for 100 randomly sampled electrodes per geometry and interpolated to 2^16 points inside the torso volume, producing approximately 6.5M training samples per electrode. Two geometry encoding strategies were compared: a linear PCA-based encoding of heart and torso shape, and a DeepSDF-based encoding, where each geometry was represented as a compact latent vector of a neural implicit signed distance function.
Results. DeepSDF-based geometry encoding outperforms PCA-based representations, resulting in lower angular errors in the lead field vectors (3.89° ± 0.51° vs. 5.22° ± 0.61°) and improved the accuracy of ECG reconstruction (relative L2 error 1.8% vs. 2.4%). Surrogate inference per electrode is approximately 25× faster than conventional FEM computation (on the same CPU hardware), with the performance gap increasing for larger electrode sets.